1

DUSTY PLASMA PHYSICSBasic Theory and Experiments

Professor Robert L. MerlinoDepartment of Physics and Astronomy

The University of IowaIowa City, IA

The Abdus Salam International Center for Theoretical PhysicsSummer College on Plasma Physics

30 July — 24 August 2007

2

CONTENTS

• Part I.— Introduction (what is a dusty plasma and where are they found)

• Part II.— Basic processes in dusty plasmas

• Part III.— Waves and instabilities in dusty plasmas

3

General references

• Shukla & Mamun, Introduction to Dusty Plasma Physics, IOP, Bristol, 2002. (SM)

• Goertz, Rev. Geophys. 27, 271, 1989. (G)• Fortov et. al., Physics Reports 421, Dec. 2005. (F)• Mendis and Rosenberg, Cosmic Dusty Plasma, Annu.

Rev. Astron. Astrophys. 32, 419, 1994. (MR)• Bouchoule, ed., Dusty Plasmas: Physics, Chemistry and

Technical Impacts in Plasma Processing, John Wiley, New York, 1999. (B)

• Plasma Sources Science & Technology, Vol. 3 Number 3, August 1994. (PSST)

• references to above sources

4

Part I.—Introduction

• what is a dusty plasma

• were are dusty plasmas– in space, astrophysics, and the lab– comets– noctilucent clouds, PMSEs– Saturn’s rings– plasma processing reactors– fusion devices

5

plasma = electrons + ions Plasma

+

-

+

+

+

+

+

+

+

- -

-

-

--

-

+

-

What is a dusty plasma?

D

• Debye shielding

dusty plasma = plasma + small particles of solid matter

• becomes negatively charged

• absorbs electrons and ions

6

Cosmic dusty plasmas (MR)

• Solar nebulae

• Planetary nebulae

• Supernova shells

• Interplanetary medium

• Molecular clouds

• Circumsolar rings

• Asteroids

7

Dusty plasmas in the solar system (G)

• Cometary tails and comae• Planetary ring systems – Saturn’s rings• Dust streams ejected from Jupiter• Zodiacal light

Dusty plasmas on the earth• Ordinary flames• Atmospheric aerosols• charged snow• lightning on volcanoes

8

Man-made dusty plasmas

• Rocket exhaust• Dust on surfaces in

space (space station)• Dust in fusion devices• Thermonuclear fireballs• Dust precipitators used

to remove pollution from smoke stacks

• Plasmas used for microelectronic fabrication, e.g. semiconductor chips, solar cells and flat panel displays

• Plasma Enhanced Chemical Vapor Deposition (PECVD) technologies

• Dusty plasma devices (DPDs) used to produce and study dusty plasmas in the laboratory

9

An early temperaturemeasurement in a dusty plasma.

A flame is a very weakly ionized plasma that contains soot particles

the high degree of ionizationin ordinary hydrocarbon flames (five orders of magnitudehigher than that predicted by theSaha equation) is due to thermionic electron emissionfrom 10 nm particles of unburnt carbon (soot)

D. A. Mendis, New Vistas inDusty Plasmas, AIP Conf. Proc.799, American Inst. Physics, Melville, N. Y. 2005, p 583.

10

Rosette Nebula ASTRONOMY

• Gravity was the focus of 20th Century Astronomy

• For the 21st Century, it will be electromagnetismand plasmas in addition

• astrophysicists now realize that the dust may be charged and that must be taken into account

Our solar systemaccumulated out of a dense

cloud of gas and dustforming everything

that is now part of our world.

11

CometHale-Bopp

(MR)

ion tail

dust tail

12

• an unusual atmospheric phenomenon occurring in the high latitude region of the earth’s summer –(–140 C) mesosphere (50 – 85 km);

• glowing, silvery white clouds of ice crystals (50 nm) at about 80 km

• usually seen just after sunset• associated with PMSE -polar mesospheric

summer echoes – unusually strong radar echoes and electron “bite-outs’

Noctilucent Clouds

13

average height of PMSEs and number of displays of NLCs

M. Rapp & F. –J. Lübken, Atmos. Chem. Phys. 4, 2601, 2004.

14

Apollo astronauts see “moon clouds”

• dust acquires a positivecharge due to solar UV

• some grains are lifted off of the moon’s surface by the electrostatic forceelectrostatically levitated

dust

http://www.space.com/scienceastronomy/061007_moon_dust.html

15

Spokes in Saturn’s B ring (G, MR)

• discovered by Voyager 2 in 1980

• nearly radial spokes rotating around the outer portion of the dense B ring

• spokes seen in forward scattered light – fine dust

• spokes exhibit dynamical behavior on timescales of minutes.

16

Semiconductor Processing (B, PSST)

silane (SiH4) + Ar + O2 SiO2 particles

17

John Goree’sLab at theUniv. of Iowa

18

Semiconductor Manufacturing (B, PSST)

dustSi

The formation of dust during the processing of semiconductorelectronics is a serious problem for the industry. It has been

estimated that up to one-half of all semiconductorchips were contaminated during processing.

20

Rocket Exhaust is a Dusty Plasma

• 0.01-10 m Al2O3 particles

• Charged dust may be trappedin earth’s B field

• Particles may reach highaltitudes and contribute toseed population for NLC

• Occurrence of NLC hasincreased over past 30 years!

Columbia Oct. 20, 1995

21

dust in fusion devices D III

22

dust particles in tokamak C Mod

23

dust in fusion devices• the “dust” is a result of the strong

interaction between the material walls and energetic plasma which causes flaking, blistering, arching and erosion of the carbon limiters or beryllium surfaces.

• one problem is that the dust may retain a large inventory of tritium

• studies indicate that dust can be transported deep into the plasma causing a serious contamination problem.

• dust poses a serious concern for ITER

24

snowy plasma• blowing snow can get charged by triboelectric

charging (friction)• both positive and negative snow has been found:

–200 C/kg and +72 C/kg.• The transport of snow along a surface is a

process called saltation. The particles hop along the surface rebounding to heights of about 10 cm. The bouncing particles are usually negative, while the particles on the surface are positive.

• the electrostatic forces on the snow may be an important consideration in avalanches.

25

Milestones in dusty plasma research

• the discovery of the spokes in Saturn’s B ring in 1980 and

• the realization of the dust contamination problem in the semiconductor processing industry at about the same time

• provided the impetus that allowed the field of dusty plasma physics to flourish.

• the discovery of the dust problem in fusion devices in1998 is another factor that continues to drive dusty plasma research

26

Part II.—Basic processes in dusty plasmas (SM, MR, F)

A. dust charging theory

B. the electrostatic potential around a dust particle

C. forces on dust particles in a plasma

D. strongly and weakly coupled dusty

E. Dusty plasmas under microgravity

F. particle growth in plasmas

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A. Dust Charging Processes

• electron, positive andnegative ion collection

• secondary emission• UV induced

photoelectron emission

Total current to an electrically floating grain = 0

I = Ie + I+ + I–+ Isec + Ipe = 0The dust particle floats to a potential at which I =0

28

• orbital motion limited (OML) ion current

The Charge on a Dust Grain

• In typical lab plasmas Isec = Ipe = 0, also take I– = 0

• Electron thermal speed >> ion thermal speed so the grains charge to a negative potential S (= Vs-Vp) relative to the plasma, until the condition Ie = Ii is achieved.

• Take spherical grains of radius aa

• electron current2

2

exp 42

1 42

e Se e

e e

i Si i

i i

kT eI en a

m kT

kT eI en a

m kT

29

Isolated vs. closely-packed dust (G, MR)

• when computing the charge Qd =eZd on dust particles we must first consider whether or not the particles can be considered as “isolated” or not.

• a single dust particle in a plasma is isolated• when many dust particles are present with a

number density nd, the dust charge will be a function of the ratio of the interparticle spacing, to the plasma Debye length, D.

1/ 3~ (3/ 4 )dn

30

A. Isolated dust particles (F)• eni = eni + Qdnd, nd 0, so ni ni

• charging equation

• define:

•

1/ 2 1/ 2

exp 1 0e i s s

i e e i

T m e e

T m kT kT

/ , / , /s s e i e e ie kT m m T T

1/ 2 1/ 2 1 0s

se

31

dust potential and charge (F)

-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

0.1 1 10 100

es/kT

e

Te

/ Ti

Argon ions

Hydrogen ions

charge

4

d d

d d s

d o

Q eZ

Q C

C a

32

Typical Laboratory Plasma

For T e = Ti = T in a hydrogen plasma,

S = 2.5 (kT/e)

If T 1 eV and a = 1 m,

Qd 2000 e

Mass, md 5 1012 mp

33

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0 2 10-6 4 10-6 6 10-6 8 10-6 1 10-5

time (s)

-150

-100

-50

0

50

0 2 10-6 4 10-6 6 10-6 8 10-6 1 10-5

electronsionstotal

time (s)

Evolution of grain charge

H+ ions, Te= 2.5 eV, Ti = 0.025 eV, ne,i = 1015 m3

/ 14

d e

e i

Td oT T d i

o

d en aV e V T

dt

16

0

1.62 10 4d e i o dq I I dt C a

34

Characteristic charging time tch

/ 2 +

15

e

~ , where are the steady state

electron and ion currents to the particle, 4

using 4 , then, for a Ar plasma2

with T 2 , 4 / , ~ 10

s e

dch o eo io

o

d o s

eV kTeeo e

e

s e e

Qt I I I

I

Q aV

kTI en e a

m

eV V kT e n

3 , 1

1 note that ~ (see Fortov, p. 1

0.16 sec

3)ch

e

ch

m a m

tn a

t m

35

Dust Charge Measurements

0

0.5

1

1.5

2

0 20 40 60 80 100 120

Diameter (micron)2

0

0.5

1

1.5

0 20 40 60 80 100 120 140 160

Electron Energy (eV)

Glass

Graphite

Walch, Horanyi, & Robertson,Phys. Rev. Lett. 75, 838 (1995)

36

Langmuir probe measurements

dust ON

time

probe current, Ie

dust off dust off

ON

eI

OFF

eI

Probe

Ie

plasma

37

Dusty Plasma Device (F61)

TO PUMP

Ta HOT PLATE

K OVEN

ROTATING DUST DISPENSER

PLASMA COLUMN

COLD END PLATE

SOLENOID COIL

Q machine

Probe

dustyplasma

38

Ieo Ie

Dust OFF

Dust ON

• When the dust is turned ON, theelectrons become attached to the dust grains and as a resulttheelectron current to the probedecreases.

• The quantity Zdnd and estimated by measuring the reduction in the electron probecurrent and using the neutralitycondition ni = ne + Zdnd, using

Zdnd = no(1 – Ie,dust/Ieo)

where no is the initial plasma density.

Langmuir probe measurements

39

close-packing effect (G)

• if many dust grains are present the charge on a single grain is reduced, usually by a large value

• this reduction is due to the fact that the grain surface potential is not only due to the charge on this grain but to all other dust grains in its vicinity

• this effect is important when the intergrain spacing D

40

close-packing effect (G)

e/kT e/kT

x/D x/D

Equally spaced infinite plane sheets of dust grains

when the electrons are shared by many particles,each particle gets a smaller portion.

42

close-packing effect: theory

1 1

2 2/ 2 2

1 1

2 2

1 0

1 /

4

/ , / , /

41 1 0

( )

s e

s

e kTe i se i

e i i

i e d e d i

o s

e i i e s s e

os s

d e

i

kT kT een e a en a

m m kT

n n Zn n Zn n

eZ a

T T m m e kT

P ee

n akTP Havnes parameter

en

43

close-packing effect: results

44

fixed nd

close-packing effect: experiment

P = ndakT/eni

(see, F61)

45

B. the electrostatic potential around a dust particle-isotropic plasma

a

r

2

2

( )

( ) / /

2

( ) , ( ) 0

( ) 0, ( )

assume Boltzmann electrons and ions with / 1

( ) ,D D

i e

o

s i

i o

e i

r a r

D

d d en n

dr r dr

a n a

n n

e kT

eZ eZr e e for a

r r

Yukawa Potential

46

electrostatic PE between particles (F18)

2 2/( ) Dr

el

e ZU r e

r

experiments

+

47

the electrostatic potential around a dust particle-with ion flow

ion density enhancement

F157-159

48

C. Forces on dust particles (F, p 40)

1) gravity: Fg = mdg = (4/3)a3 d g

where d is the density of the dust material,

typically ~ 1000 – 2000 kg/m3

for thin-walled hollow microspheres of wall

thickness t, md 4a2t

49

2) electric force: Fe = QdE

can be used to levitate negative particles:

md g

QdE

-VE

for a 1 micron particlemd ~ 8x10-15 kgQ ~ -2000emdg = QdE

E = mdg/Qd ~ 2.5 V/cm

50

3) neutral drag force: Fnd (F, p. 46)

ud = dust velocity, vT,n = gas thermal speed, N = gas density

(a) ud >> vT,n

(b) ud << vT,n

2 2

nd n dF a Nm u

2

,

8

3n

nd d d T n

d

mF m u a N v

m

where 1<<2 is a factor that depends on how the atomsare scattered on the dust surface.

dust-neutral collision frequency, dn

51

This force arises if there is a temperature gradient in the neutral gas. It is due to the asymmetry in the momentum transfer to dust from neutrals and is directed toward lower gas temperatures. This force can be used to levitate particles against gravity.

2

,

n ,

4 2

15

where is the thermal conductivity coefficient of the gas,

which for atomic gases 1.33 / , where is the

cross-section for neutral-neutral collisions

th n n

T n

n

T n nn nn

aF T

v

v

4) thermophoresis force: FTh (F, p 46)

52

• This force arises from the momentum transfer from flowing ions to charged microparticles in a plasma.

• This can be one of the most important forces that gives rise to particle transport in dusty plasmas.

• Ion flows are usually produced by large scale electric fields that typically exist in plasmas.

5) Ion drag force, Fid (F, p41)

53

dustcollected ions

deflected ions

id ic ioF F F

Collection force due toions impinging on grain

Orbit force due toions deflected by grain

5) Ion drag force, Fid, continued

54

2

1

22

1

2

2

(a) collection force,

simplified theory of Barnes et. al. (F198)

ion drift speed

8where , mean ion speed

2and 1 , collision impact

ic

i

ic i i i s c

is i

i

sc

i s

F

u

F n m u u b

kTu u

m

eb a

m u

parameter

5) Ion drag force, Fid, continued

55

2

/ 2

/ 2 2

2 2

/ 2

2 2

/ 2

(b) orbit force

4

where , impact parameter for 90 collisions4

1and ln , Coulomb logarithm (up to )

2

io

io i i i s

d

o i s

DD

c

F

F n m u u b

eQb

m u

b

b b

5) Ion drag force, Fid, continued

56

VD, ID

Laser

Langmuirprobe

DustDropper

Filaments

Levitationplate

Magnets

ions

• glass microspheres falling through the plasma are deflected by ions which acquire drift due to a weak ambipolar electric field in the plasma• the ion drag force is determined from the measured deflection angles

5) Ion drag force: experimental measurements

57

exp. results – ion drag

58

D. Weakly vs. strongly coupled dusty plasmas (F, p 69)

• The fundamental characteristics of a many-particle interacting system is the coupling constant

2 2

o

o

potential energy of interation between particles

average kinetic energy of the particles

Q 4=

4

where is the average interparticle spacing, usually

taken to be the Wigner-Seit

Q

kT kT

1/ 34

z radius 3

where n is the particle density

n

59

(a) Weakly coupled plasma

15 3

6

23

Consider a typical laboratory plasma with a density

10 , and electron temperatrure 2

For this plasma, 6 10 .

The resulting potential and kinetic energies are:

4 10 and

en m T eV

m

PE J

19

4

3.2 10 ,

coupling constant 10 1.

This is an example of a weakly coupled plasma.

Most "ordinary' plasmas are weakly coupled.

ekT J

60

(a) Strongly coupled plasma

4

d

4

Consider now a typical laboratory dusty plasma

with a = 5 m, 140 , 2 , 0.03

In this case Q 10

Now, 10 1

This is a strongly coupled dusty plasma

e dm T eV T eV

e

61

Factors that contribute to making dusty plasmas strongly coupled

• Qd = eZd, with high Zd (~103 – 104), ~ Z2

• Dust grains are easily cooled to near room temperature by neutral gas interactions

• Dynamic time scales for microparticle relaxation in a plasmas are relatively short compared to colloidal systems.

62

Classification of many-particle systems

class phase

<< 1 weakly coupled

gas

~ 1 ? liquid

>> 1 strongly coupled

solid

By varying it is possible to study thephase transitions in a strongly coupled

dusty plasma crystal

63

APSCent_S1dataPhase Diagram of a Yukawa System

100

1000

10000

0.0 1.0 2.0 3.0 4.0 5.0

solid (fcc)

solid (bcc)

fluid

D

Condition for forming a “dust crystal” 171

F370, 372, 373

64

Experimental observation of strongly coupled dusty plasmas

Coulomb crystals (F11-14)• In 1986, Ikezi gave theoretical arguments

indicating that a Coulomb lattice of small particles could be produced. He discussed the conditions for solidification.

• In 1994, 4 experimental groups (MPE, Taiwan, Japan, Kiel Univ.) announced the observation of Coulomb solids in RF parallel plate discharges (GEC cells).

65

RF plasma discharges (PSST)

13.56 MHz Ez

QE

mg

Ez

particles

V(r)

dust shaker

sheaths

V(z)

z

0

Er Er

66

RF Dusty Plasma Device

67

Coulomb CrystalJohn Goree – Univ. Iowa

triangular lattice with hexagonal symmetry

68

The particles arevertically aligned due to the downwardion flow

Ion flow

A plasma crystal having multiple layers

69

BGAS

IN

Hot Plate Cs Plasma

Rotating DustDispenser

DustBall

AnodeGlow

Anode

VideoCamera

Barkan and Merlino, Phys. Plasmas 2, 3261, 1995.

Observation of the Dust Balls

70

1 cm

ANODE

Dust (Coulomb) Ball

71

coulomb explosion

electrostatically confineddust ball at t = 0

electrostatically confinementsuddenly turned off

t = 0

t = 1/30 s

t = 2/30 s

The electrostatic confinement isturned off by turning the plasmaoff. With the plasma off, there isno Debye shielding. This causesthe dust to experience a largerepulsive force leading to anacceleration of almost 3 g’s

72

Coulomb Balls

effect of thermophoretic force

73Arp, Block, Piel & Melzer, PRL, 15 Oct. 2004

Dust Coulomb Balls

74

Melting of a Plasma Crystal

Melzer, Homann, and Piel, PRE 53, 2747 (1996)

75

• The pair correlation function g(r)

represents the probability of finding 2 particles separated by adistance r.• It is a measure of the translational order in structures.• For a crystal at T = 0, g(r) is a series of equally spaced delta functions.

r

1( ) ( ) ,

= # particles, ,

N

i ji j

j

g r r r rN

N r r positions

Melting

76

Melting a crystal by heating

= 4000

* = 10.6

* = 2.7

*

/ D

e

Nonomura at al, PRL 94, 045001, 2005

77

It is possible to diagnose dusty plasmas down to the particle level

• In a dusty plasma, it is possible to follow the position and velocity of all the particles as a function of time [r(t), v(t)].

• This is not possible in ordinary plasmas where, at best we can determine the distribution function of the ions and electrons

78

Crystallization fronts in complex plasmas(Rubin-Zuzic et al Nature physics 2, 181, 2006)

107 melamine formaldehyde particles (1.28 m) in an rf discharge at 173 mTorr.Images are 16 s apart. The crystal was melted down by a sudden decrease inthe rf power and subsequently allowed to re-freeze.

79

E. Dusty plasmas under microgravity (F20,21,34,37)

• In the earth-based laboratory, it is necessary to use a levitation method to keep microparticles from falling.

• In the RF dusty plasma devices, the particles always reside in the sheath region and usually in 2D structures.

• The PKE Nefedov device is an RF plasma system operating in the microgravity environment on the International Space Station (ISS)

80

PKE Nefedov device on ISS

81

PKE Nefedov schematic

82

VOID

Voids in dusty plasmas under microgravity

Void is due to the outward ion dragforce on the microparticles

83

F. Particle growth in plasmas(PSST, B)

• Nanoparticles and microparticles can be grown in a plasma.

• This can occur in plasma reactors used in semiconductor etching and deposition systems using reactive chemical species like silane, SiH4:

• e– + SiH4 (SiH4)* SiH2 + 2 H

• {Caution: I know less about this topic than all other topics in these lectures. }

84

particle growth kinetics

85

A 650 nm particle grown in an helium rf plasma with carbon electrodes

86

particle growth kinetics

IG: initial growth phase

RG: rapid growth phase

SG: saturated growth phase

particle size

particle density

IG RG SG

time (s)

10 20 30

50 nm

1015 m-3

87

three phases of particle growth in silane plasmas

88

particle growth mechanisms

• Initial growth: nucleation of reactive anions, cations and neutrals in the gas phase (stoms & molecules)

from < nm few nm• Rapid growth: agglomeration or coagulation

phase, this qualifies as dusty plasma

10 nm 100 nm,• Saturated growth: growth at constant density by

surface deposition of SiHx

100 nm m

89

reactions involved in IG phase

The initial precursors forparticle growth are thoughtto be heavy, singly chargednegative ion clusters.

90

Cosmic dust growth by coagulation

• coagulation is a random growth process whereby particles can stick together via mutual collisions forming larger particles.

• this can occur in the presolar nebula, circumstellar, circumplanetary, cometary, etc. environments

• however, if the grains all have the like charge, coagulation can not take place unless the grains can overcome their mutual Coulomb repulsion

91

overcoming Coulomb repulsion

12 2

2

d ,

relative velocity v of two grains of charge q,

mass m, radius a required:

v2

for H plasma with T = 2 eV, a = 0.5

v 2 /

for dust at T 1 , v 10 / ,

coagulation is imp

o

d T

q

am

m

m s

eV m s

ossible

92

A cosmic dust growth scenario

M. Horanyi and C. Goertz (Ap. J. 361, 155, 1990)

• found a scenario in which grains of opposite polarity might be formed leading to enhanced coagulation

• How to get positively charged grains:– photoemission in radiative environment– secondary electron emission energetic

electrons

• need a mechanism that gives both positive and negative gains

93

effect of secondary electron emission (SEE) and temperature fluctuations

• in presence of SEE, grain potential is multi-valued (Meyer-Vernet 1982)

• charging time ~ a–1

• consider case of grains of various sizes in plasma with temp. fluctuations– big grains positive– small grains negative

• enhanced coagulation

Equ

ilibr

ium

gra

in

pote

ntia

l

0

Plasma Temperature

N. Meyer-Vernet, AstronAstrophys. 105, 98 (1982)

94

Electrostatic disruption (MR)

• Dust growth must compete with the tendency of highly charged grains to be blown apart by the electrostatic tension

• Electrostatic disruption will occur unless the tensile strength of the material exceeds the electric force Ft > Fe (~ 2/a2)

• Disrupting grains will continue to do so

• Effect is circumvented by field emission of electrons from negative grains

95

Part III.—Waves and instabilities in dusty plasmas (SM, MR, F)

F.Verheest, Space Sci. Rev., 77, 267, 1996)

A. effect of dust on collective processes

B. methods of analysis of dusty plasma waves

C. fundamental wave modes in dusty plasmas (1) unmagnetized plasma

(a) dust ion acoustic wave (DIA)

(b) dust acoustic wave (DAW)

(2) magnetized plasma

(a) electrostatic dust ion cyclotron wave (EDIC)

(b) electrostatic dust cyclotron wave (EDC)

96

Part III.—Waves and instabilities in dusty plasmas

D. New wave damping mechanisms

(1) “Tromsø damping”

(2) “creation damping”

E. Waves in strongly coupled dusty plasmas

(1) compressional modes

(2) shear modes

(3) Mach cones

97

Effect of dust on collective processes in plasmas -1

• consider the case in which there is a significant amount of dust in the plasma

• the presence of negatively charged dust can affect the properties of plasma waves even for waves with frequencies high enough that the dust does not participate in the wave motion (dust is an immobile neutralizing background)

• this is because the dust affects the charge neutrality condition: en+ = ene + Qdnd

98

• the presence of charged dust leads to modifications in the wave dispersion relations [real (K)]

• the dust can also affect instability conditions (growth rates, critical drifts, etc.)

• for frequencies below the characteristic plasma frequencies, new “dust modes” emerge, these are modes in which the dust participates in the wave motion.

Effect of dust on collective processes in plasmas -2

99

• Although the effect of dust on plasma waves is similar to the effects that occur in plasmas with negative ions, there are important differences:– the charge on the dust may not be constant– there may be a distribution of dust sizes,

leading to a distribution of mass and charge.– the dust may be in a liquid or crystalline state

Effect of dust on collective processes in plasmas -3

100

Analysis of dusty plasma waves

• the theoretical analysis of wave modes and major instabilities in a dusty plasma can be performed by considering the dust species as another fluid component which obeys the usual continuity and momentum equations

v0

v vv v v

d dd

d d dd d d d d d d d

nn

t xn

m n kT en Zt x x x

101

kinetic theory ofdusty plasma waves

• the standard Vlasov analysis of plasma waves and instabilities can also be applied to dusty plasmas

• the dust is assumed to have a Maxwellian velocity distribution

• instability analyses can also be carried out by using drifting Maxwellians

102

Fundamental wave modes in a dusty plasma

• unmagnetized plasma– dust ion acoustic (DIA) mode– dust acoustic wave (DAW)

• magnetized plasma– electrostatic dust ion cyclotron wave (EDIC)– electrostatic dust cyclotron wave (EDC)

R. L. Merlino, et. al., Phys. Plasmas 5, 1607, 1998

103

Dust ion acoustic mode (DIA)Shukla and Silin, Physica Scripta 45, 508, 1992

1 10

1 1 10 0

1 0 1

1 1 1

0 0 0 0 0

1, long wavelength limit

v0

v

0

/ /

, 0 (dust immobile

IONS

EL

)

ECTRO

, /

NS:

D

e e e

e d

e d d

K

nn

t xn

m n kT ent x xn n e kT

n n n

n n Zn n n

104

phase velocity of DIA wave

1

2

1

2,

,

(1 )

percentage of negative

charge on the dust

1

e

DIA

e eff

DIA

DIA

ee eff

kT kT Z

K m

Z

kT kTC

K m

TT

Z

Z

v ph / v ph(=0)

10

1

105

DIA -comments

• the effect of dust is to increase the phase velocity of the ion acoustic waves

• this can be interpreted formally as an increase in the effective electron temperature which has important consequences for wave excitation

• Ion acoustic waves are subject to ion Landau damping, which is severe for Te ~ T+, however the effect of the dust is to increase the phase speed which has the effect of decreasing the Landau damping, since now the wave-particle resonance at v+,th ~ vph no longer holds with vph>> v+,th

106

1.0

1.1

1.2

1.3

1.4

1.5

PH

AS

E V

EL

OC

ITY

0 0.5 1Zd

(a)

DIA

phas

e sp

eed ki/kr

0.0

0.5

1.0

Ki/K

r

0 0.5 1Zd

DIA

(b)

LANGMUIR PROBE Ta Hot Plate

rotating dustdispenser

end plateprobe

K oven

launching grid

Dust Ion Acoustic Wave Experiment

107

Dust ion acoustic shocks

• Normally in a plasma with Te = T+ a compressive pulse will not steepen into a shock-like structure because of Landau damping

• However, in a dusty plasma, DIA waves are subject to insignificant Landau damping, so that shock formation should be possible

108

Experimental setup

CsBHP EP

LP

RotatingDust Dispenser

n

z

(a)

(b)

G

PG

109

DIA Shocks – results

110

DIA Shocks – results

111

Dust acoustic (DA) waves(Rao, Shukla, Yu, Planet. Space. Sci. 38, 543, 1990)

• very low frequency (<< p+, phase speed Csd << v+,th) longitudinal compressional disturbances in a fluid-like dusty plasma

• the dust particles participate in the wave dynamics – it is a “dust wave”

• phase speed (dust acoustic speed)

2~DA

d

kTC Z

m

112

Dust acoustic waves: fluid theory

2

( )0

0

0; 0

( )( )

d d d

d d dd d d d d d

ee e

o e d

e d d

n n v

t xv v n

m n v kT eZ nt x x x

n nkT en kT en

x x x x

e n n Zn

n n Z n

Dustdynamics

Quasineutrality

Electrons& Ions

1DdK

113

Combining the dust momentum equation with the plasma equations we see that (for the case of cold dust, Td = 0).

( )dd d e

vm n P P

t x

where Pe + P+ is the total pressure due toelectrons and ions.

In the dust acoustic wave the inertia isprovided by the massive dust particles and the electrons and ions provide the restoring force

daw-2

114

excitation of dust acoustic waves

• dust acoustic waves can be driven by an ion-dust streaming instability (Rosenberg, JVST A 14, 631, 1996)

• a relatively modest drift uo~ vith of the ions through the dust is sufficient for instability

• DAWs are spontaneously excited in dusty plasmas produced in gas discharges

• are observed visually by laser light scattering

115

id

DA

e

d

nn

C

ZTT

Z

m

kT

K

:where

21

2

11

222

21

22

2

111

1

DiDeD

D

DA

K

C

K

:where

dust acoustic dispersion relationship (Td ~ 0)

Finite Deffects:

K

Effect of dust-gas collisions:

is the dust-neutral collision frequency

2 2

DAi K C

acoustic modes (long wavelength)

116

wavefronts

Dust Acoustic Wave Image

117

Dust acoustic waves

Measurement of the dispersion relationship of the dust acoustic wave

Original ExperimentsA. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Plasmas, 2, 3563 (1995). C. Thompson, A. Barkan, N. D’Angelo, and R. L. Merlino, Phys. Plasmas, 4, 2331 (1997).

cm

118

UI dusty plasma device

300 – 400 V~ 1 mA

B

Ar, 50 -150 mtorr

ANODELASER

DUST

Parameters

plasma density ~ 108 – 109 cm-3 Te ~ 2 – 3 eV, T+ ~ 0.025 eV Dust: kaolin powder -average dust radius ~ 1 micron average dust charge Z ~ – (1000 – 2000) dust density nd ~ 105 cm-3, pd ~ 300 - 500 s-1

ANODEGLOW

For current modulation

119

60 cm dia. x 80 cm long vacuum vesseldc glow discharge plasmas (N2, Ar)50 - 100 G axial magnetic fields

Dust acoustic waves are captured using a 30 fps digital camera

Experiment at Univ. of Iowa, Fall, 2006

120

single frame video images of DAW

65 kHz

130 kHz

Natural

39 kHzinterferenceeffects

121

video analysis

About 100 images were analyzed for each frequency

122

dispersion relation short wavelengths

(

s–1)

(

s–1

)

K (cm–1)

Td = 40 eV

Td = 10 eV

123

Magnetized plasma—Electrostatic dust ion cyclotron waves (EDIC)

2 2 2

2 2 2

(1 )i e

cii i d

ci DIA

kT kTK

m m Z

K C

• Electrostatic ion-cyclotron waves excited by electron current along the magnetic field• dust is treated as an immobile charge neutralizing background• waves propagate at large angle to B (K >> K||)

124

Electrostatic dust ion-cycloton instability (EDIC)

Amplitude of EIC Waverelative to case with no dust

125

EDIC- kinetic theory results

V. W. Chow & M. Rosenberg, Planet. Space Sci. 44, 465 (1996)

1/(1 )dZ

v de/v

e,th

• EIC instability driven by current along B• As more negative charge is carried by the dust, the critical drift needed to excite the instability decreases• the instability is easier to excite in a dusty plasma

Critical electrondrift velocity

126

Electrostatic dust cyclotron mode (EDC)

• EDIC – involves cyclotron motion of the dust – magnetized dust

• Dispersion relation

2 2 2 2

2 2 2

1

1 ( / )(1 )d

cd dd i e d

cd DA

kTK Z

m T T Z

K C

127

Gyroradius of dust particles

,

3

1

2

,

8

, ,

d dd

d

dd T

d

d d

d

m vr

eZ B

kTv

m

m a Z a

r a

10-4

10-3

10-2

10-1

100

0.001 0.01 0.1 1 10

Rd (m) [Td=0.025 eV]Rd(m) (Td=1.0 eV)Rd (m) [Td = 0.1 eV]

Dust radius, m

B = 1 T

1 cm

1 mm

Dus

t gy

rora

dius

, m

128

New damping mechanisms for DAWand DIA waves

(1) Tromso damping due to Dust charge fluctuations—[Melandso, Aslaksen and Havnes,

Planet. Space Sci. 41, 321, 1993]. In the presence of plasma potential oscillations, the charge on the dust will also oscillate. If the frequency of the potential fluctuations is close to the dust charging frequency (inverse of dust charging time) this can lead to a damping. The damping of the wave is due to the delay in charging the particles.

129

(2) Creation damping — [D’Angelo, Planet. Space Sci. 42, 507, 1994]. This is a damping due to the fact that plasma which is absorbed on the dust must be replaced by a continuous injection of new plasma by ionization. The newly created ions do not share initially in the wave motion of the existing ions and hence lower the average momentum of the ion population. This can be an important damping mechanism for the DIA wave.

130

Waves in strongly coupled dusty plasmas (F, p. 58)

• The presence of short scale correlations gives rise to novel modifications of the collective behavior

• Both compressional and transverse shear waves are possible

• dispersion relations are derived from the equations of motion

,

( )

neutral drag coeff., k = spring constants

Njk jk jk jk

d dm m k

131

Compressional and shear waves

132

Dispersion of DAW in strong coupling regime (Piper& Goree PRL 77, 3137, 1996)

In this case better agreement was obtained with the dispersionrelation derived from fluid theory – ignoring the strong coupling.

133

Laser excited dust lattice waves in plasma crystals (Homan et al PLA 242, 173, 1998)

In this case the data agreed with the results of the dust lattice wave. Themain difference was that this exp. had a single dust layer not multiple ones.

134

Observation of the transverse shear wave in a strongly coupled dusty plasma (Pramanik et al, PRL 88, 175001, 2002)

135

Mach cones in dusty plasmas (F 254, 255)

Mach cones are V-shaped disturbances (shock waves) produced by supersonic a object moving through a medium

V 1sin sC

V M

Havnes et. al. (J. Geophys. Res. 100, 1731, 1995) proposed to look forMach cones in Saturn’s rings during the Cassini mission

136

The cones were produced by supersonically moving particles just below the dust crystal

Mach cones observed in the lab Samsonov, et al., PRE 61, 5557,2000

137

Mach cone observations

particle velocity map

grey-scale speed map

grey-scale number density map

138

summary of Mach cone data

139

Future directions in dusty plasma research

• dust does not necessarily have only undesirable consequences– use plasma technologies to produce powders with control over

size, composition and structure– modify surface properties using materials grown in plasmas

• use dusty plasma systems to study “nano-dynamics” -behavior of systems at the kinetic level, e.g., physics of liquids, phase transitions, etc.

• explore consequences of the understanding that particle growth takes place in plasmas both in cosmos and lab

• Transfer our detailed understanding of basic properties of dusty plasmas acquired through theory and in the lab to astrophysical plasmas